出版社：Institute for Operations Research and the Management Sciences (INFORMS), Applied Probability Society
摘要：We consider the simulation-based solution of linear systems ofequations, Ax = b, of various types frequently arising in large-scaleapplications, where A is singular. We show that the convergence prop-erties of iterative solution methods are frequently lost when they areimplemented with simulation (e.g., using sample average approxima-tion), as is often done in important classes of large-scale problems.We focus on special cases of algorithms for singular systems, includ-ing some arising in least squares problems and approximate dynamicprogramming, where convergence of the residual sequence {Axk. b}may be obtained, while the sequence of iterates {xk} may diverge.For some of these special cases, under additional assumptions, weshow that the iterate sequence is guaranteed to converge. For situa-tions where the iterates diverge but the residuals converge to zero, wepropose schemes for extracting from the divergent sequence anothersequence that converges to a solution of Ax = b
